Advertisements
Advertisements
Question
The conjugate of the complex number `(1 - i)/(1 + i)` is ______.
Advertisements
Solution
The conjugate of the complex number `(1 - i)/(1 + i)` is ______.
Explanation:
`(1 - i)/(1 + i) = (1 - i)/(1 + i) xx (1 - i)/(1 - i)`
= `(1 + i^2 - 2i)/(1 - i^2)`
= `(1 - 1 - 2i)/(1 + 1)`
= –i
Hence, conjugate of `(1 - i)/(1 + i)` is i.
APPEARS IN
RELATED QUESTIONS
Find the modulus and argument of the complex number `(1 + 2i)/(1-3i)`
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.
Find the conjugate of the following complex number:
4 − 5 i
Find the conjugate of the following complex number:
\[\frac{1}{3 + 5i}\]
Find the conjugate of the following complex number:
\[\frac{1}{1 + i}\]
Find the conjugate of the following complex number:
\[\frac{(3 - i )^2}{2 + i}\]
Find the conjugate of the following complex number:
\[\frac{(1 + i)(2 + i)}{3 + i}\]
Find the conjugate of the following complex number:
\[\frac{(3 - 2i)(2 + 3i)}{(1 + 2i)(2 - i)}\]
Find the modulus of \[\frac{1 + i}{1 - i} - \frac{1 - i}{1 + i}\].
Find the modulus and argument of the following complex number and hence express in the polar form:
1 + i
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\sqrt{3} + i\]
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1 - i}{1 + i}\]
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1}{1 + i}\]
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{- 16}{1 + i\sqrt{3}}\]
If (1+i)(1 + 2i)(1+3i)..... (1+ ni) = a+ib,then 2 ×5 ×10 ×...... ×(1+n2) is equal to.
If \[x + iy = (1 + i)(1 + 2i)(1 + 3i)\],then x2 + y2 =
Solve the equation `z^2 = barz`, where z = x + iy.
If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (–4, 0), find the greatest and least values of |z + 1|.
If a complex number lies in the third quadrant, then its conjugate lies in the ______.
If z1 = `sqrt(3) + i sqrt(3)` and z2 = `sqrt(3) + i`, then find the quadrant in which `(z_1/z_2)` lies.
What is the conjugate of `(sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) - sqrt(5 - 12i))`?
If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then find arg`(z_1/z_4)` + arg`(z_2/z_3)`.
Solve the system of equations Re(z2) = 0, z = 2.
State True or False for the following:
If z is a complex number such that z ≠ 0 and Re(z) = 0, then Im(z2) = 0.
What is the conjugate of `(2 - i)/(1 - 2i)^2`?
If `(a^2 + 1)^2/(2a - i)` = x + iy, what is the value of x2 + y2?
sinx + icos2x and cosx – isin2x are conjugate to each other for ______.
